Implementing the three-particle quantization condition for π+π+K+ and related systems
Abstract Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theor...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2022
|
| Online Access: | https://hdl.handle.net/1721.1/140549.2 |
| _version_ | 1811090327076864000 |
|---|---|
| author | Blanton, Tyler D. Romero-López, Fernando Sharpe, Stephen R. |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Blanton, Tyler D. Romero-López, Fernando Sharpe, Stephen R. |
| author_sort | Blanton, Tyler D. |
| collection | MIT |
| description | Abstract
Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude
K
$$ \mathcal{K} $$
df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to
O
$$ \mathcal{O} $$
(1/L5); and we calculate the leading-order predictions in chiral perturbation theory for
K
$$ \mathcal{K} $$
df,3 in the π+π+K+ and π+K+K+ systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π+π+K+ levels using the two- and three-particle interactions predicted by chiral perturbation theory. |
| first_indexed | 2024-09-23T14:42:43Z |
| format | Article |
| id | mit-1721.1/140549.2 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:42:43Z |
| publishDate | 2022 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/140549.22024-06-07T20:11:47Z Implementing the three-particle quantization condition for π+π+K+ and related systems Blanton, Tyler D. Romero-López, Fernando Sharpe, Stephen R. Massachusetts Institute of Technology. Center for Theoretical Physics Abstract Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K $$ \mathcal{K} $$ df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O $$ \mathcal{O} $$ (1/L5); and we calculate the leading-order predictions in chiral perturbation theory for K $$ \mathcal{K} $$ df,3 in the π+π+K+ and π+K+K+ systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π+π+K+ levels using the two- and three-particle interactions predicted by chiral perturbation theory. 2022-02-22T20:42:21Z 2022-02-22T13:45:07Z 2022-02-22T20:42:21Z 2022-02 2022-01 2022-02-20T04:20:58Z Article http://purl.org/eprint/type/JournalArticle 1029-8479 https://hdl.handle.net/1721.1/140549.2 Journal of High Energy Physics. 2022 Feb 14;2022(2):98 en https://doi.org/10.1007/JHEP02(2022)098 Journal of High Energy Physics Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/octet-stream Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Blanton, Tyler D. Romero-López, Fernando Sharpe, Stephen R. Implementing the three-particle quantization condition for π+π+K+ and related systems |
| title | Implementing the three-particle quantization condition for π+π+K+ and related systems |
| title_full | Implementing the three-particle quantization condition for π+π+K+ and related systems |
| title_fullStr | Implementing the three-particle quantization condition for π+π+K+ and related systems |
| title_full_unstemmed | Implementing the three-particle quantization condition for π+π+K+ and related systems |
| title_short | Implementing the three-particle quantization condition for π+π+K+ and related systems |
| title_sort | implementing the three particle quantization condition for π π k and related systems |
| url | https://hdl.handle.net/1721.1/140549.2 |
| work_keys_str_mv | AT blantontylerd implementingthethreeparticlequantizationconditionforppkandrelatedsystems AT romerolopezfernando implementingthethreeparticlequantizationconditionforppkandrelatedsystems AT sharpestephenr implementingthethreeparticlequantizationconditionforppkandrelatedsystems |